My wife and I had a kaiseki dinner at Gion Maruyama (http://gionmaruyama.com/) in Kyoto last year and it was one of the best meals of our lives. There are two locations, we ate at the one closest to Maruyama Park and sat at the counter. As soon as we left we were anticipating our next visit. In Tokyo we had another top five meal at Takazawa (http://www.aroniadetakazawa.com/).
Just a couple of suggestions from someone who’s only been to Japan once for two weeks. There are so many incredible restaurants, I know there are dozens of other fantastic choices. Enjoy your trip!